Justification Patterns for OWL DL Ontologies

For debugging OWL-DL ontologies, natural language explanations of inconsistencies and undesirable entailments are of great help. From such explanations, ontology developers can learn why an ontology gives rise to specific entailments. Unfortunately, commonly used tableaux-based reasoning services do not provide a basis for such explanations, since they rely on a refutation proof strategy and normalising transformations that are difficult for human ontology editors to understand. For this reason, we investigate the use of automatically generated justifications for entailments (i.e., minimal sets of axioms from the ontology that cause entailments to hold). We show that such justifications fall into a manageable number of patterns, which can be used as a basis for generating natural language explanations by associating each justification pattern with a rhetorical pattern in natural language

Completing and Debugging Ontologies: state of the art and challenges

As semantically-enabled applications require high-quality ontologies, developing and maintaining ontologies that are as correct and complete as possible is an important although difficult task in ontology engineering. A key step is ontology debugging and completion. In general, there are two steps: detecting defects and repairing defects. In this paper we discuss the state of the art regarding the repairing step. We do this by formalizing the repairing step as an abduction problem and situating the state of the art with respect to this framework. We show that there are still many open research problems and show opportunities for further work and advancing the field.Comment: 56 page

Measuring the understandability of deduction rules for OWL

Debugging OWL ontologies can be aided with automated reasoners that generate entailments, including undesirable ones. This information is, however, only useful if developers understand why the entailments hold. To support domain experts (with limited knowledge of OWL), we are developing a system that explains, in English, why an entailment follows from an ontology. In planning such explanations, our system starts from a justification of the entailment and constructs a proof tree including intermediate statements that link the justification to the entailment. Proof trees are constructed from a set of intuitively plausible deduction rules. We here report on a study in which we collected empirical frequency data on the understandability of the deduction rules, resulting in a facility index for each rule. This measure forms the basis for making a principled choice among alternative explanations, and identifying steps in the explanation that are likely to require extra elucidation

RaDON - Repair and Diagnosis in Ontology Networks

One of the major challenges in managing networked and dynamic ontologies is to handle inconsistencies in single ontologies, and inconsistencies introduced by integrating multiple distributed ontologies. Our RaDON system provides functionalities to repair and diagnose ontology networks by extending the capabilities of existing reasoners. The system integrates several new debugging and repairing algorithms, such as a relevance-directed algorithm to meet the various needs of the users

A Lightweight Defeasible Description Logic in Depth: Quantification in Rational Reasoning and Beyond

Description Logics (DLs) are increasingly successful knowledge representation formalisms, useful for any application requiring implicit derivation of knowledge from explicitly known facts. A prominent example domain benefiting from these formalisms since the 1990s is the biomedical field. This area contributes an intangible amount of facts and relations between low- and high-level concepts such as the constitution of cells or interactions between studied illnesses, their symptoms and remedies. DLs are well-suited for handling large formal knowledge repositories and computing inferable coherences throughout such data, relying on their well-founded first-order semantics. In particular, DLs of reduced expressivity have proven a tremendous worth for handling large ontologies due to their computational tractability. In spite of these assets and prevailing influence, classical DLs are not well-suited to adequately model some of the most intuitive forms of reasoning. The capability for abductive reasoning is imperative for any field subjected to incomplete knowledge and the motivation to complete it with typical expectations. When such default expectations receive contradicting evidence, an abductive formalism is able to retract previously drawn, conflicting conclusions. Common examples often include human reasoning or a default characterisation of properties in biology, such as the normal arrangement of organs in the human body. Treatment of such defeasible knowledge must be aware of exceptional cases - such as a human suffering from the congenital condition situs inversus - and therefore accommodate for the ability to retract defeasible conclusions in a non-monotonic fashion. Specifically tailored non-monotonic semantics have been continuously investigated for DLs in the past 30 years. A particularly promising approach, is rooted in the research by Kraus, Lehmann and Magidor for preferential (propositional) logics and Rational Closure (RC). The biggest advantages of RC are its well-behaviour in terms of formal inference postulates and the efficient computation of defeasible entailments, by relying on a tractable reduction to classical reasoning in the underlying formalism. A major contribution of this work is a reorganisation of the core of this reasoning method, into an abstract framework formalisation. This framework is then easily instantiated to provide the reduction method for RC in DLs as well as more advanced closure operators, such as Relevant or Lexicographic Closure. In spite of their practical aptitude, we discovered that all reduction approaches fail to provide any defeasible conclusions for elements that only occur in the relational neighbourhood of the inspected elements. More explicitly, a distinguishing advantage of DLs over propositional logic is the capability to model binary relations and describe aspects of a related concept in terms of existential and universal quantification. Previous approaches to RC (and more advanced closures) are not able to derive typical behaviour for the concepts that occur within such quantification. The main contribution of this work is to introduce stronger semantics for the lightweight DL EL_bot with the capability to infer the expected entailments, while maintaining a close relation to the reduction method. We achieve this by introducing a new kind of first-order interpretation that allocates defeasible information on its elements directly. This allows to compare the level of typicality of such interpretations in terms of defeasible information satisfied at elements in the relational neighbourhood. A typicality preference relation then provides the means to single out those sets of models with maximal typicality. Based on this notion, we introduce two types of nested rational semantics, a sceptical and a selective variant, each capable of deriving the missing entailments under RC for arbitrarily nested quantified concepts. As a proof of versatility for our new semantics, we also show that the stronger Relevant Closure, can be imbued with typical information in the successors of binary relations. An extensive investigation into the computational complexity of our new semantics shows that the sceptical nested variant comes at considerable additional effort, while the selective semantics reside in the complexity of classical reasoning in the underlying DL, which remains tractable in our case

Generating Natural Language Explanations For Entailments In Ontologies

Building an error-free and high-quality ontology in OWL (Web Ontology Language)---the latest standard ontology language endorsed by the World Wide Web Consortium---is not an easy task for domain experts, who usually have limited knowledge of OWL and logic. One sign of an erroneous ontology is the occurrence of undesired inferences (or entailments), often caused by interactions among (apparently innocuous) axioms within the ontology. This suggests the need for a tool that allows developers to inspect why such an entailment follows from the ontology in order to debug and repair it. This thesis aims to address the above problem by advancing knowledge and techniques in generating explanations for entailments in OWL ontologies. We build on earlier work on identifying minimal subsets of the ontology from which an entailment can be drawn---known technically as justifications. Our main focus is on planning (at a logical level) an explanation that links a justification (premises) to its entailment (conclusion); we also consider how best to express the explanation in English. Among other innovations, we propose a method for assessing the understandability of explanations, so that the easiest can be selected from a set of alternatives. Our findings make a theoretical contribution to Natural Language Generation and Knowledge Representation. They could also play a practical role in improving the explanation facilities in ontology development tools, considering especially the requirements of users who are not expert in OWL

Module extraction for inexpressive description logics

Module extraction is an important reasoning task, aiding in the design, reuse and maintenance of ontologies. Reasoning services such as subsumption testing and MinA extraction have been shown to bene t from module extraction methods. Though various syntactic traversal-based module extraction algorithms exist for extracting modules, many only consider the subsumee of a subsumption statement as a selection criterion for reducing the axioms in the module. In this dissertation we extend the bottom-up reachability-based module extraction heuristic for the inexpressive Description Logic EL, by introducing a top-down version of the heuristic which utilises the subsumer of a subsumption statement as a selection criterion to minimize the number of axioms in a module. Then a combined bidirectional heuristic is introduced which uses both operands of a subsumption statement in order to extract very small modules. We then investigate the relationship between MinA extraction and bidirectional reachabilitybased module extraction. We provide empirical evidence that bidirectional reachability-based module extraction for subsumption entailments in EL provides a signi cant reduction in the size of modules for almost no additional costs in the running time of the original algorithms.Computer ScienceM. Sc. (Computer Science